Geosci. Model Dev., 14, 2419–2442, 2021 https://doi.org/10.5194/gmd-14-2419-2021 © Author(s) 2021. This work is distributed under the Creative Commons Attribution 4.0 License.

BFM17 v1.0: a reduced biogeochemical flux model for upper-ocean biophysical simulations

Katherine M. Smith1, Skyler Kern1, Peter E. Hamlington1, Marco Zavatarelli2, Nadia Pinardi2, Emily F. Klee3, and Kyle E. Niemeyer3 1Paul M. Rady Department of Mechanical Engineering, University of Colorado, Boulder, CO, USA 2Department of Physics and Astronomy, University of Bologna, Bologna, Italy 3School of Mechanical, Industrial, and Manufacturing Engineering, Oregon State University, Corvallis, OR, USA

Correspondence: Katherine M. Smith ([email protected])

Received: 9 May 2020 – Discussion started: 13 July 2020 Revised: 19 February 2021 – Accepted: 2 March 2021 – Published: 5 May 2021

Abstract. We present a newly developed upper-thermocline, provides improved correlations between several model out- open-ocean biogeochemical flux model that is complex and put fields and observational data, indicating that reproduc- flexible enough to capture open-ocean ecosystem dynamics tion of in situ data can be achieved with a low number of but reduced enough to incorporate into highly resolved nu- variables, while maintaining the functional group approach. merical simulations and parameter optimization studies with Notable additions to BFM17 over similar complexity models limited additional computational cost. The model, which are the explicit tracking of dissolved oxygen, allowance for is derived from the full 56-state-variable Biogeochemical non-Redfield nutrient ratios, and both dissolved and partic- Flux Model (BFM56; Vichi et al., 2007), follows a bio- ulate organic matter, all within the functional group frame- logical and chemical functional group approach and allows work. for the development of critical non-Redfield nutrient ratios. Matter is expressed in units of carbon, nitrogen, and phos- phate, following techniques used in more complex models. To reduce the overall computational cost and to focus on 1 Introduction upper-thermocline, open-ocean, and non-iron-limited or non- silicate-limited conditions, the reduced model eliminates cer- Biogeochemical (BGC) tracers and their interactions with tain processes, such as benthic, silicate, and iron influences, upper-ocean physical processes, from basin-scale circula- and parameterizes others, such as the bacterial loop. The tions to millimeter-scale turbulent dissipation, are critical for model explicitly tracks 17 state variables, divided into phy- understanding the role of the ocean in the global carbon cy- toplankton, zooplankton, dissolved organic matter, particu- cle. These interactions cause multi-scale spatial and tempo- late organic matter, and nutrient groups. It is correspondingly ral heterogeneity in tracer distributions (Strass, 1992; Yoder called the Biogeochemical Flux Model 17 (BFM17). After et al., 1992; McGillicuddy et al., 2001; Gower et al., 1980; describing BFM17, we couple it with the one-dimensional Denman and Abbott, 1994; Strutton et al., 2012; Clayton, Princeton Ocean Model for validation using observational 2013; Abraham, 1998; Bees, 1998; Mahadevan and Archer, data from the Sargasso Sea. The results agree closely with 2000; Mahadevan and Campbell, 2002; Levy and Klein, observational data, giving correlations above 0.85, except for 2015; Powell and Okubo, 1994; Martin et al., 2002; Ma- chlorophyll (0.63) and oxygen (0.37), as well as with corre- hadevan, 2005; Tzella and Haynes, 2007) that can greatly sponding results from BFM56, with correlations above 0.85, affect carbon exchange rates between the atmosphere and except for oxygen (0.56), including the ability to capture interior ocean, net primary productivity, and carbon export the subsurface chlorophyll maximum and bloom intensity. (Lima et al., 2002; Schneider et al., 2008; Hauri et al., 2013; In comparison to previous models of similar size, BFM17 Behrenfeld, 2014; Barton et al., 2015; Boyd et al., 2016). There are still significant gaps, however, in our understand-

Published by Copernicus Publications on behalf of the European Geosciences Union. 2420 K. M. Smith et al.: A reduced biogeochemical flux model ing of how these biophysical interactions develop and evolve, plexity and severely truncating the number of equations thus limiting our ability to accurately predict critical ex- used to describe the dynamics of an ecosystem. Such ap- change rates. proaches include the well-known nutrient–phytoplankton– Better understanding these interactions requires accurate zooplankton–detritus class of models. These models have physical and BGC models that can be coupled together. The significantly fewer unknown parameters and can be more exact equations that describe the physics (e.g., the Navier– easily integrated within complex physical models. Their sim- Stokes or Boussinesq equations) are often known and physi- plicity also enables greater transparency when attempting to cally accurate solutions can be obtained given sufficient spa- understand the dominant forcing or dynamics underlying a tial resolution and computational resources. Due to the vast particular event. While they are often capable of reproducing diversity and complexity of ocean ecology, however, even the overall distributions of chlorophyll, primary production, when only considering the lowest trophic levels, accurately and nutrients (Anderson, 2005), such simplified models have modeling BGC processes can be quite difficult. Put simply, been shown to underperform at capturing complex ecosys- there are no known first-principle governing equations for tem dynamics, and often struggle in regions of the ocean for ocean biology. which they were not calibrated (Friedrichs et al., 2007). As such, two different approaches to modeling BGC pro- Although both of these general BGC modeling approaches cesses are often used when faced with this challenge. The have their respective advantages, particularly given their dif- first is to increase model complexity and include equations ferent objectives, the difference between lower-complexity for every known BGC process. Often, these models include BGC models used in small-scale studies and the more com- species functional types or multiple classes of phytoplank- plex BGC models used in global ESMs poses a problem. ton and/or zooplankton that each serve specific functional In particular, the difficulty in directly comparing the two roles within the ecosystem, such as calcifiers or nitrogen fix- types of models makes the process of “scaling up” newly de- ers. The justification for this approach is that particular phy- veloped parameterizations or “downscaling” BGC variables toplankton and zooplankton groups serve as important sys- within nested-grid studies much more challenging. This mo- tem feedback pathways, and that without explicit represen- tivates the need for a new BGC model that is reduced enough tation of these feedbacks, there is little hope of accurately to be usable within high-resolution, high-fidelity physical representing the target ecosystem (Doney, 1999; Anderson, simulations for process, parameterization, and parameter op- 2005). In many cases, these models also contain variable timization studies but is still complex enough to capture im- intra- and extracellular nutrient ratios, which are important portant ecosystem feedback dynamics, as well as the dynam- when accounting for different nutrient regimes within the ics of vastly different ecosystems throughout the ocean, as global ocean and species diversity of non-Redfield nutrient required by ESMs. ratio uptake (Dearman et al., 2003). To begin addressing this need, here we present a Although these more complex models are typically highly new upper-thermocline, open-ocean, 17-state-variable Bio- adaptable and are often able to capture different dynamics geochemical Flux Model (BFM17) obtained by reducing than those for which they were calibrated (Blackford et al., the larger 56-state-variable Biogeochemical Flux Model 2004; Friedrichs et al., 2007), these more complex models (BFM56) developed by Vichi et al.(2007). Most high- contain many more parameters than their simplified coun- fidelity, high-resolution physical models are capable of inte- terparts. Moreover, many of the parameters, such as phy- grating 17 additional tracer equations with limited additional toplankton mortality, zooplankton grazing rates, and bacte- computational cost. Following the approach used in BFM56 rial remineralization rates, are inadequately bounded by ei- (Vichi et al., 2007, 2013), a biological and chemical func- ther observational or experimental data (Denman, 2003). Be- tional family (CFF) approach underlies BFM17, where mat- cause of the increased complexity of such models, it is also ter is exchanged in the model through units of carbon, nitrate, often difficult to ascertain which processes are responsible and phosphate. This permits variable non-Redfield intra- and for the development of a particular event (e.g., a phytoplank- extracellular nutrient ratios. Most notably, BFM17 includes ton bloom), and so these models can be ill suited for process a phosphate budget, the importance of which has historically studies. Lastly, while these highly complex models are reg- been underappreciated even though observational data have ularly used within global Earth system models (ESMs), they indicated its potential importance as a limiting nutrient, par- are typically prohibitively expensive to integrate within high- ticularly in the Atlantic Ocean (Ammerman et al., 2003). To fidelity, high-resolution physical models. Examples of such reduce model complexity, we parameterize certain processes models are those used to enhance fundamental understanding for which field data are lacking, such as bacterial remineral- of subgrid-scale (SGS) physics in ESMs and to assist in the ization. development of new SGS parameterizations (Roekel et al., In the present study, we outline, in detail, the formula- 2012; Hamlington et al., 2014; Suzuki and Fox-Kemper, tion of BFM17 and its development from BFM56. We cou- 2015; Smith et al., 2016, 2018). ple BFM17 to the 1-D Princeton Ocean Model (POM) and In broad terms, the second common BGC modeling ap- validate the model for upper-thermocline, open-ocean condi- proach is focused on substantially decreasing model com- tions using observational data from the Sargasso Sea. We also

Geosci. Model Dev., 14, 2419–2442, 2021 https://doi.org/10.5194/gmd-14-2419-2021 K. M. Smith et al.: A reduced biogeochemical flux model 2421 compare results from BFM17 and the larger BFM56 for the pendixA. Results from a zero-dimensional (0-D) test of same upper-thermocline, open-ocean conditions. As a result BFM17 are provided in AppendixB. In Sect.3, BFM17 is of the focus on upper-thermocline, open-ocean conditions, coupled to the 1-D POM physical model. A discussion of the further assumptions have been made in deriving BFM17 methods used to calibrate and validate the model with ob- from BFM56, such as the exclusion of any representation for servational data collected in the Sargasso Sea is presented in the benthic system and the absence of limiting nutrients such Sect.4. Model results, a skill assessment, a comparison to as iron and silicate. results from BFM56, and a brief comparison to other similar It should be noted that the primary focus of the present BGC models are discussed in Sect.5. study is to introduce the viability of BFM17 as an accurate BGC model for high-resolution, high-fidelity simulations of the upper ocean used in process, parameterization, and pa- 2 Biogeochemical Flux Model 17 (BFM17) rameter optimization studies. This is accomplished here by comparing results from BFM17 to results from observations The 17-state equation (BFM17) is an upper-thermocline, and BFM56; as such, here we only consider one open-ocean open-ocean BGC model derived from the original 56-state location (i.e., the Sargasso Sea). Although the model must equation model (BFM56) (Vichi et al., 2007, 2013), which also be applied at other locations to determine its general ap- is based on the CFF approach. In this approach, functional plicability, its ability to reproduce important and difficult key groups are partitioned into living organic, non-living organic, behaviors in the Sargasso Sea supports its use as a process and non-living inorganic CFFs, and exchange of matter oc- study model. The correspondence between BFM17 and the curs through constituent units of carbon, nitrogen, and phos- more general BFM56 also provides confidence that the re- phate. To date, there are no other BGC models with this or- duced model will prove effective at modeling other ocean der of reduced complexity using the CFF approach, making locations and conditions, and exploring the range of appli- BFM17 unique and able to accurately reproduce complex cability of BFM17 remains an important direction for future ecosystem dynamics. research. We also emphasize that relatively limited calibra- BFM17 is a pelagic model intended for oligotrophic re- tion of BFM17 parameters has been performed in the present gions that are not iron or silicate limited and is obtained study. Most parameters are set to their values used in the from the more-complete BFM56 by omitting quantities and larger BFM56 (Vichi et al., 2007, 2013), and optimization of processes assumed to be of minor importance in these re- these parameters over a range of ocean conditions is another gions. We have developed BFM17 primarily for use with important direction of future research, for which BFM17 is high-resolution, high-fidelity numerical simulations, includ- ideally suited. ing large eddy simulations (LESs) used in process, parame- Finally, we note that other similarly complex BGC models terization, and parameter optimization studies. As such, we have been calibrated using data from the Sargasso Sea, such do not validate the efficacy of BFM17 as a global BGC as those developed in Levy et al.(2005), Ayata et al.(2013), model, and note that it is missing potentially important pro- Spitz et al.(2001), Doney et al.(1996), Fasham et al.(1990), cesses for such an application, which we elaborate on shortly. Fennel et al.(2001), Hurtt and Armstrong(1996), Hurtt and We also note that we compare BFM17 to the original BFM56 Armstrong(1999), and Lawson et al.(1996). However, each in Sect.5 to demonstrate that, although it is reduced in com- of these models employs less than 10 species and none use plexity, BFM17 is equally appropriate for use in seasonal a CFF approach or include oxygen, a tracer that is histor- process, parameterization, and optimal parameter estimation ically difficult to predict. Although some of these models studies for which a more complex model such as BFM56 employ data assimilation techniques (e.g., Spitz et al., 2001) may be too computationally expensive. Nevertheless, given and produce relatively accurate results, most leave room for the agreement between the BFM17 and BFM56 results in improvement. With a minimal increase in the number and Sect.5, there is reason to believe that BFM17 may have po- complexity of the model equations, such as those associ- tential as a global BGC model, and the examination of the ated with tracking phosphate in addition to carbon and ni- broader applicability of BFM17 is an important direction for trate, and by including both particulate and dissolved organic future research. nutrient budgets, we anticipate that a significant increase in In BFM17, the living organic CFF is comprised of single- model accuracy and applicability might be achieved over pre- phytoplankton and zooplankton living functional groups vious models of similar complexity. Additionally, with this (LFGs); these two groups are the bare minimum needed increase in model complexity, the disparate gap between the within a BGC model and already account for six state equa- complexity of BGC models used in small- and global-scale tions (corresponding to carbon, nitrogen, and phosphate con- studies is reduced, thereby simplifying up- and down-scaling stituents of both groups). The baseline parameters used in efforts. This last point is emphasized here by the good agree- BFM17 are those detailed in Vichi et al.(2007), and a ment between results from BFM17 and BFM56. complete list of the model parameters is provided in Ap- In the following, BFM17 is introduced in Sect.2, with pendixA. Parameters used in the representation of phyto- detailed equations and parameter values provided in Ap- plankton loosely correspond to the flagellate LFG in BFM56, https://doi.org/10.5194/gmd-14-2419-2021 Geosci. Model Dev., 14, 2419–2442, 2021 2422 K. M. Smith et al.: A reduced biogeochemical flux model while the zooplankton parameters correspond to the micro- within the upper thermocline of the open ocean, the ecosys- zooplankton LFG. The only relevant difference with respect tem is not substantially influenced by a benthic system and to Vichi et al.(2007) is related to the choice of the phyto- any water-column influences from depth can be taken into ac- (0) plankton specific photosynthetic rate (rP in Table A3 of Ap- count using boundary conditions (such as those discussed in pendixA); in this case, the new value was chosen according Sect.4). As such, we cannot attest to the accuracy of BFM17 to the control laboratory cultures of Fiori et al.(2012). in shelf or coastal regions. Within BFM17, we track chlorophyll, dissolved oxygen, In summary, notable novel attributes of BFM17, in com- phosphate, nitrate, and ammonium, since their distributions parison to other models of comparable complexity, are the and availability can greatly enhance or hinder important bio- use of (i) CFFs for living organisms, including two LFGs for logical and chemical processes. Dissolved oxygen is of par- phytoplankton and zooplankton, (ii) CFFs for both particu- ticular interest, because it is historically difficult to predict late and dissolved organic matter, (iii) a full nutrient profile using BGC models of any complexity. This is likely due, in (i.e., phosphate, nitrate, and ammonium), and (iv) the track- part, to missing physical processes in the mixing parameter- ing of dissolved oxygen. A summary of the 17 state variables izations used in global and column models. This provides tracked in BFM17 is provided in Table1, and a schematic of motivation for the present study, since a primary goal in the the CFFs and LFGs used in BFM17, along with their inter- development of BFM17 is to create a BGC model that can be actions, is shown in Fig.1. The detailed equations compris- used in combination with high-resolution, high-fidelity phys- ing BFM17, as well as all associated parameter values, are ical models (e.g., those found in LES) to understand the ef- presented in AppendixA. Results from an initial 0-D test of fects of these physical processes and how they can be more BFM17 are provided in AppendixB. accurately represented in mixing parameterizations. Dissolved and particulate organic matter, each with their own partitions of carbon, nitrogen, and phosphate, are also 3 Coupled physical–biogeochemical flux model included in BFM17 to account for nutrient recycling and car- bon export due to particle sinking. Another primary goal of As a demonstration of BFM17 for predicting ocean biogeo- developing BFM17 is to explore how spatially decoupled (or chemistry in oligotrophic pelagic zones, here we couple the “patchy”) processes, such as the sinking of organic matter model to a 1-D physical mixing parameterization and make and the subsequent upwelling of multiple recycled nutrients comparisons with available observational data in the Sar- (not just nitrate) affect the fate and distribution of a phyto- gasso Sea. In order to focus on the upper-thermocline, open- plankton bloom. ocean regime for which BFM17 was developed, the physical Lastly, remineralization of nutrients is provided by param- model only extends 150 m in depth and diagnostically calcu- eterized bacterial closure terms, thereby reducing complexity lates diffusivity terms based upon prescribed temperature and while still maintaining critical nutrient recycling. The related salinity profiles from the observations. While a 1-D physical parameter values (see Table A5 in AppendixA) were chosen model is unlikely to resolve all processes relevant for biogeo- according to Mussap et al.(2016), who carried out sensitiv- chemistry in the upper thermocline, we have made additions, ity tests to evaluate the many parameter values found in the such as large-scale general circulation and mesoscale eddy literature. vertical velocities, as well as relaxation bottom boundary Iron is omitted from BFM17, limiting the applicability of conditions for nutrient upwelling, to better represent missing the model in regions where iron components are important, processes. such as the Southern Ocean and the tropical Pacific. Thus, For all equations here and in AppendixA, we adopt the if used in such regions, at least a fixed concentration of iron same notation style used for BFM56 in Vichi et al.(2007), may be needed (although this method has not yet been val- Mussap et al.(2016), and the BFM user manual (Vichi et al., idated within BFM17). Top-down control of the ecosystem 2013) for consistency and clarity. The coupled physical and in the form of explicit predation of zooplankton is also not BGC model is a time–depth model that integrates in time the included. Instead, a simple constant zooplankton mortality generic equation for all biological state variables, denoted is used, as this is a complicated process and understand- Aj , given by ing where to add this closure and where to feed the partic- ∂Aj ∂Aj h (set)i ∂Aj ulate and dissolved nutrients from this process in a lower- = − W + WE + v complexity model is not well understood. However, the ad- ∂t ∂t bio ∂z   dition of a top-down closure term was tested, and no ma- ∂ ∂Aj + K , (1) jor differences were observed in the model results. Conse- ∂z H ∂z quently, it was assumed that the constant mortality term was sufficient for this model, similar to other models of this com- where Aj are the 17 state variables of BFM17, the first term plexity (Fasham et al., 1990; Lawson et al., 1996; Clainche on the right-hand side accounts for sources and sinks within et al., 2004). Additionally, the benthic system within BFM56 each species due to biological and chemical reactions (as (Mussap et al., 2016) has been removed. It is assumed that represented by the equations comprising BFM17 and out-

Geosci. Model Dev., 14, 2419–2442, 2021 https://doi.org/10.5194/gmd-14-2419-2021 K. M. Smith et al.: A reduced biogeochemical flux model 2423

Table 1. Notation used for the 17 state variables in the BFM17 model, as well as the chemical functional family (CFF), units, description, and rate equation reference for each state variable. CFFs are divided into living organic (LO), non-living organic (NO), and inorganic (IO) families.

Symbol CFF Units Description Equation −3 PC LO mg C m Phytoplankton carbon (A5) −3 PN LO mmol N m Phytoplankton nitrogen (A6) −3 PP LO mmol P m Phytoplankton phosphorus (A7) −3 Pchl LO mg Chl a m Phytoplankton chlorophyll (A8) −3 ZC LO mg C m Zooplankton carbon (A31) −3 ZN LO mmol N m Zooplankton nitrogen (A32) −3 ZP LO mmol P m Zooplankton phosphorus (A33) (1) −3 RC NO mg C m Dissolved organic carbon (A41) (1) −3 RN NO mmol N m Dissolved organic nitrogen (A42) (1) −3 RP NO mmol P m Dissolved organic phosphorus (A43) (2) −3 RC NO mg C m Particulate organic carbon (A44) (2) −3 RN NO mmol N m Particulate organic nitrogen (A45) (2) −3 RP NO mmol P m Particulate organic phosphorus (A46) −3 O IO mmol O2 m Dissolved oxygen (A47) N(1) IO mmol P m−3 Phosphate (A48) N(2) IO mmol N m−3 Nitrate (A49) N(3) IO mmol N m−3 Ammonium (A50)

Figure 1. Schematic of the 17-state-equation BFM17 model. The dissolved organic matter, particulate organic matter, and living organic matter CFFs are each comprised of three chemical constituents (i.e., carbon, nitrogen, and phosphorus). The living organic CFF is further subdivided into phytoplankton and zooplankton living functional groups (LFGs).

https://doi.org/10.5194/gmd-14-2419-2021 Geosci. Model Dev., 14, 2419–2442, 2021 2424 K. M. Smith et al.: A reduced biogeochemical flux model lined in AppendixA), W and WE are the vertical veloci- gradients and temperature are used in place of potential tem- ties due to large-scale general circulation and mesoscale ed- perature since we consider only the upper water column. (set) dies, respectively, v is the settling velocity, and KH is A detailed description of POM can be found in Blumberg the vertical eddy diffusivity. Although the BFM17 formula- and Mellor(1987), and in the following we simply provide tion and model results are the primary focus of the present a description of the physical model and equations solved in study, we also perform coupled physical–BGC simulations POM-1D. In diagnostic mode, as used in the present study, using BFM56 for comparison. Equation (1) applies to all 17 POM-1D solves the momentum equations for U and V given state variables in BFM17, as well as to all 56 state variables by in BFM56. Consequently, the only differences between the biophysical models with BFM17 and BFM56 are the num- ∂U ∂  ∂U  − f V = K , (2) ber of state variables being tracked and the equations used ∂t ∂z M ∂z to calculate the biological forcing terms. The specific forms ∂V ∂  ∂V  of Eq. (1) for each of the 17 species in BFM17 are dis- + f U = KM , (3) ∂t ∂z ∂z cussed in AppendixA, and the specific forms of this equation for each of the 56 species in BFM56 were previously dis- where f = 2sinφ is the Coriolis force,  is the angular ve- cussed in Vichi et al.(2007). The parameters used in BFM56 locity of the Earth, and φ is the latitude. The vertical viscos- correspond to the values provided in Tables A3–A5 of Ap- ity KM and diffusivity KH are calculated using the closure pendixA, with the remaining undefined parameters (since hypothesis of Mellor and Yamada(1982) as BFM56 includes many more model parameters than BFM17) based on values from Mussap et al.(2016). KM = q l SM , (4) The range of values for W and W in Eq. (1) is included in E = Table2 and the corresponding depth profiles are discussed in KH q l SH , (5) Sect. 4.3. The settling velocity, v(set), in Eq. (1) is only non- zero for the three constituents of particulate organic matter, where q is the turbulent velocity and SH and SM are stability and its value is given in Table2. We assume v(set) = 0 for functions written as zooplankton, since zooplankton actively swim and oppose h i S [1 − 9A A G ] − S (18A2 + 9A A )G their own sinking velocity. Finally, KH in Eq. (1) is calcu- M 1 2 H H 1 1 2 H lated by the model and is described in more detail later in = A 1 − 3C − 6A /B  , (6) this section. 1 1 1 1 − + =  −  To obtain the complete 1-D biophysical model, BFM17 SH [1 (3A2B2 18A1A2)GH ] A2 1 6A1/B1 . (7) has been coupled with a modification of the three- dimensional (3-D) POM (Blumberg and Mellor, 1987) that The coefficients in the above expressions are = considers only the vertical (specifically, the upper 150 m of (A1,B1,A2,B2,C1) (0.92,16.6,0.74,10.1,0.08), with the water column) and time dimensions; that is, the evolution l2 g ∂ρ of the system in the (z,t) space. It is well known that the G = , H 2 (8) primary calibration dimension in marine ocean biogeochem- q ρ0 ∂z istry is along the vertical direction, as shown in several pre- −3 −2 vious calibration and validation exercises (Vichi et al., 2003; where ρ0 = 1025 kg m , g = 9.81 m s . Following Mellor Triantafyllou et al., 2003; Mussap et al., 2016). (2001), GH is limited to have a maximum value of 0.028. The 1-D POM solver (POM-1D) is used to calculate the The equation of state relating ρ to T and S is non-linear vertical structure of the two horizontal velocity components, (Mellor, 1991) and given by denoted U and V , the potential temperature, T , salinity, − − S, density, ρ, turbulent kinetic energy, q2/2, and mixing ρ = 999.8 + (6.8 × 10 2 − 9.1 × 10 3T length scale, `. In this model adaptation, vertical tempera- + 1.0 × 10−4T 2 − 1.1 × 10−6T 3 + 6.5 × 10−9T 4)T ture and salinity profiles are imposed from given climatolog- −3 −5 2 ical monthly profiles obtained from observations, as previ- + (0.8 − 4.1 × 10 T + 7.6 × 10 T ously done in Mussap et al.(2016) and Bianchi et al.(2005). − 8.3 × 10−7T 3 + 5.4 × 10−9T 4)S POM-1D directly computes the time evolution of the hori- + (−5.7 × 10−3 + 1.0 × 10−4T zontal velocity components, the turbulent kinetic energy and the mixing length scale, all of which are used to compute − 1.6 × 10−6T 2)S1.5 + 4.8 × 10−4S2 , (9) the turbulent diffusivity term, KH , required in Eq. (1). In this configuration, POM-1D is called “diagnostic” since temper- where the polynomial constants have been written only up ature and salinity are prescribed. Furthermore, pressure ef- to the first digit. For a more precise reproduction of these fects are neglected in the density equation and the buoyancy constants, the reader is referred to Mellor(1991). Finally, the governing equations solved to obtain the turbulence variables

Geosci. Model Dev., 14, 2419–2442, 2021 https://doi.org/10.5194/gmd-14-2419-2021 K. M. Smith et al.: A reduced biogeochemical flux model 2425

Table 2. Values, units, and descriptions for parameters used in the combined physical–BFM17 model.

Symbol Value Units Description v(set) −1.00 m d−1 Settling velocity of particulate detritus W −0.02–0 m d−1 Imposed general circulation vertical velocity −1 WE 0–0.1 m d Imposed mesoscale circulation vertical velocity −1 λO 0.06 m d Relaxation constant for oxygen at bottom −1 λN(1) 0.06 m d Relaxation constant for phosphate at bottom −1 λN(2) 0.06 m d Relaxation constant for nitrate at bottom q2/2 and ` are For all variables except oxygen, surface boundary condi- tions for the coupled model variable Aj are ∂ q2  ∂  ∂ q2  = K ∂t ∂z q ∂z ∂Aj 2 2 KH = 0. (16) " # ∂z = ∂U 2 ∂V 2 z 0 + K + M ∂z ∂z By contrast, the surface boundary condition for oxygen has the form g ∂ρ q3 + KH − , (10) ∂O ρ ∂z B ` KH = 8O , (17) 0 1 ∂z   z=0 ∂  2  ∂ ∂  2  q ` = Kq q ` 8 ∂t ∂z ∂z where O is the air–sea interface flux of oxygen computed according to Wanninkhof(1992, 2014). The bottom (i.e., " 2 2# ∂U  ∂V  greatest depth) boundary conditions for phytoplankton, zoo- + E `K + 1 M ∂z ∂z plankton, dissolved organic matter, and particulate organic matter are g ∂ρ q3 + − E1` KH W,e (11) ∂Aj ρ0 ∂z B1 KH = 0. (18) ∂z z=zend where Kq = κ KH is the vertical diffusivity for turbu- lence variables, κ = 0.4 is the von Karman constant, and This boundary condition was chosen since it allows removal  2 2 2 of the scalar quantity A through the bottom boundary of We = 1 + E2` /κ (1/|z| + 1/|z − H|) with (E1,E2) = j (1.8,1.33). In Eqs. (10) and (11), the time rate of change the domain. This can be seen by integrating Eq. (1) over the of the turbulence quantities is equal to the diffusion of turbu- boundary layer depth using the boundary condition above, lence (the first term on the right-hand side of both equations), giving the shear and buoyancy turbulence production (second and z=0 Z third terms), and the dissipation (the fourth term). This is a ∂ h (set)i Aj dz = W + WE + v Aj , (19) second-order turbulence closure model that was formulated ∂t z=zend = by Mellor(2001) as a particular case of the Mellor and Ya- z zend mada(1982) model for upper-ocean mixing. where the biological part of Eq. (1) has been neglected and Boundary conditions for the horizontal velocities U = the resulting temporal change in the integrated scalar Aj is (set) (U,V ) and the turbulence quantities are negative since |(W +WE)| < |v |, as shown in Table2. For oxygen, phosphate, and nitrate, the bottom boundary condi- ∂U KM = τ w , (12) tions are ∂z z=0 ∂A   ∂U j = − ∗ = KH λj Aj z=z Aj , (20) KM 0, (13) ∂z = end ∂z z=zend z zend    |τ |  ∗ 2 2 = 2/3 w where λj and Aj are the corresponding relaxation velocity q ,q ` B1 ,0 , (14) z=0 Cd and observed at-bottom boundary climatological field data 2 2 value, respectively, of that species. Base values for the relax- (q ,q `)|z=z = 0, (15) end ation velocities are included in Table2. Lastly, the bottom where τ w = Cd|uw|uw is the surface wind stress, uw is the boundary condition for ammonium is surface wind vector, Cd is a constant drag coefficient chosen (3) . × −3 z = z = z ∂N to be 2 5 10 , and 0 and end denote the locations KH = 0. (21) of the surface and the greatest depth modeled, respectively. ∂z z=zend https://doi.org/10.5194/gmd-14-2419-2021 Geosci. Model Dev., 14, 2419–2442, 2021 2426 K. M. Smith et al.: A reduced biogeochemical flux model

Since observations of ammonium concentration in the ob- for the BATS data and 23 years (not continuous) for the BTM servational area are not available, this choice is based on data. Additionally, we interpolate the BATS data to a verti- the assumption that the nitrogen diffusive flux from depth cal grid with 1 m resolution. We subsequently smooth the in- to the surface (euphotic) layers occurs mostly in the form of terpolated data, using a robust locally estimated scatterplot a nitrate flux, consistent with the concepts of “new” and “re- smoothing (LOESS) method, to maintain a positive buoy- generated” production, as described by Dugdale and Goering ancy gradient, thereby eliminating any spurious buoyancy- (1967) and Mulholland and Lomas(2008). driven mixing due to interpolation and averaging. Figure2 shows the monthly climatological profiles of tem- perature and salinity from the BATS data (maximum mixed 4 Field validation and calibration data layer depth from the climatology is approximately 149 m, which was calculated based upon a 0.2 kgm−3 increase in 4.1 Study site description density from the surface value), as well as the PAR and Field data for calibration and validation of BFM17 10 m wind speed from the BTM data. The same monthly are taken from the Bermuda Atlantic Time-series Study averaging, vertical interpolations, and smoothing used for (BATS) (Steinberg et al., 2001) and the Bermuda Testbed the physical variables are also performed for biological vari- Mooring (BTM) (Dickey et al., 2001) sites, which are lo- ables, which largely serve as target fields for the validation cated in the Sargasso Sea (31◦400 N, 64◦100 W) in the North of BFM17. Atlantic subtropical gyre. Both sites are a part of the US Joint 4.3 Inputs to the physical model Global Ocean Flux Study (JGOFS) program. Data have been collected from the BATS site since 1988 and from the BTM The physical model computes density from the prescribed site since 1994. temperature and salinity, and surface wind stress from the Steinberg et al.(2001) provide an overview of the biogeo- 10 m wind speed; temperature, salinity, and wind speed are chemistry in the general BATS and BTM area. Winter mixing all provided by the BATS/BTM data. The model also uses allows nutrients to be brought up into the mixed layer, pro- these data in the turbulence closure to compute the turbulent ducing a phytoplankton bloom between January and March viscosity and diffusivity. This diagnostic approach eliminates (winter mixed layer depth is typically 150–300 m). As ther- any drifts in temperature and salinity that might occur due to mal stratification intensifies over the summer months, this improper parameterizations of lateral mixing in a 1-D model, nutrient supply is cut off (summer mixed layer depth is typi- therefore providing greater reliability. In addition to the 10 m cally 20 m). At this point, a subsurface chlorophyll maximum wind speed, temperature, and salinity, BFM requires monthly is observed near a depth of 100 m. Stoichiometric ratios of varying PAR at the surface. For all the monthly mean input carbon, nitrate, and phosphate are often non-Redfield and, in datasets, a correction (Killworth, 1995) is applied. This cor- contrast to many oligotrophic regimes, phosphate is the dom- rection is applied to the monthly averages to reduce the er- inant limiting nutrient (Fanning, 1992; Michaels et al., 1993; rors incurred by linearly interpolating monthly averages to Cavender-Bares et al., 2001; Steinberg et al., 2001; Ammer- the much shorter model time step. man et al., 2003; Martiny et al., 2013; Singh et al., 2015). We imposed both general circulation, W, and mesoscale eddy, W , vertical velocities in the simulations. The imposed 4.2 Data processing E vertical profiles of these velocities have been adapted from The region encompassing the BATS and BTM sites is char- Bianchi et al.(2005), where the velocities are assumed to acterized as an open-ocean oligotrophic region that is phos- be zero at the surface and reach their maxima near the base phate limited. This region has thus been chosen for ini- of the Ekman layer, which is assumed to be at or below the tial testing of BFM17 due to the prevalence of oligotrophic bottom boundary of the simulations. The general large-scale regimes in the open ocean and to demonstrate the ability upwelling or downwelling circulation, W, is due to Ekman of BFM17 to capture difficult non-Redfield ratio regimes pumping and is correspondingly given as (which occur in phosphate-limited regions). The BATS/BTM τ  W = kˆ · ∇ × w , (22) data have also been collected over many years, providing ρf long time series for model calibration and validation. Data from the BATS/BTM area are used in the present where kˆ denotes the unit vector in the vertical direction. study for two purposes: (i) as initial, boundary, and forc- The monthly average value and sign of the wind stress curl, ing conditions for the POM-1D biophysical simulations with ∇ × τ w, for the general BATS/BTM region is taken from the BFM17 and BFM56, and (ii) as target fields for validation of Scatterometer Climatology of Ocean Winds database (Risien the simulations. In addition to the subsurface BATS data, we and Chelton, 2008, 2011). The monthly value of W from also use BTM surface data, such as the 10 m wind speed and Eq. (22) is then assumed to be the maximum, occurring at photosynthetically active radiation (PAR). For each observa- the base of the Ekman layer, for that particular month. Given tional quantity, we compute monthly averages over 27 years the sign of the wind stress curl for the BATS/BTM region, a

Geosci. Model Dev., 14, 2419–2442, 2021 https://doi.org/10.5194/gmd-14-2419-2021 K. M. Smith et al.: A reduced biogeochemical flux model 2427

Figure 2. Sargasso Sea physical variables, showing climatological monthly averaged (a) temperature, (b) 10 m surface wind speed, (c) surface PAR, and (d) salinity. Panel (e) shows the mean seasonal general circulation velocity, W, and panel (f) shows the bimonthly maximum value −3 of the mesoscale eddy velocity WE. Monthly averaged mixed layer depths (defined as the depth at which the density is 0.2 kgm greater than the surface density) are shown as black lines in panel (a). negative W was calculated, indicating general downwelling termined either through the adoption of the Redfield ratio processes in this region. Seasonal profiles of W are shown in C : N : P ≡ 106 : 16 : 1 (Redfield et al., 1963) or assuming a Fig.2e. reasonably low initial value. Since the 1-D simulations were Due to the prevalence of mesoscale eddies within the run to steady state over 10 years, memory of these initial BATS/BTM region (Hua et al., 1985), which can provide states was assumed to be lost, with little effect on the results. episodic upwelling of nutrients to the upper water column, For the comparison of BFM17 to BFM56, the initial con- we also include an additional positive upwelling vertical ve- ditions for the additional state variables were calculated by locity, WE, which has a timescale of 15 d. The general profile splitting the total initial phytoplankton and zooplankton car- of WE is assumed to be the same as for W, with a value of bon values into equal amounts for all phytoplankton and zoo- zero at the surface and a maximum value at depth. However, plankton groups. The other state variables for each group there is no linear interpolation between each 15 d period, and were again calculated using the Redfield ratio. The initial the maximum magnitude of WE is randomized between 0 and bacteria distribution was defined by setting the column equal 0.1 md−1, as shown in Fig.2f for each 15 d period. to a constant value. In both simulations, the bottom boundary conditions for 4.4 Initial and boundary conditions oxygen, nitrate, and phosphate species are based on observed BATS data. Values are taken at the next closest data point Although the BATS/BTM data include information on many below the bottom boundary (at 150 m) and then averaged biological variables, initial conditions for only 5 of the 17 over the month. Figure3b shows the monthly average bot- species within BFM17 could be extracted from the data. Sim- tom boundary conditions for each of the three species. ilarly to the temperature and salinity, the initial chlorophyll, particulate organic nitrogen, oxygen, nitrate, and phosphate were interpolated to a mesh with 1 m vertical grid spacing, 5 Model assessment results averaged over the initial month of January, and smoothed vertically in space to give the initial profiles seen in Fig.3a. The coupled BFM17-POM-1D model was run using the pa- The remaining 12-state-variable initial conditions were de- rameter values from Tables2, A1, and A3–A5, which were https://doi.org/10.5194/gmd-14-2419-2021 Geosci. Model Dev., 14, 2419–2442, 2021 2428 K. M. Smith et al.: A reduced biogeochemical flux model

Figure 3. Sargasso Sea initial and boundary conditions showing (a) initial profiles of nitrate, phosphate, particulate organic carbon, chloro- phyll, and oxygen, where each profile, denoted φi(z), is normalized by its depth averaged value, hφiiz, and (b) monthly bottom boundary conditions for nitrate, phosphate, and oxygen, where each quantity, ϕi(t), is normalized by its annual average value hϕiit . The depth and annual averaged values are shown in parentheses in the legends of each panel. Units are mmol N m−3 for nitrate, mmol P m−3 for phosphate, mg C m−3 for particulate organic carbon, mg Chl m−3 for chlorophyll, and mmol O m−3 for oxygen. decided on the basis of standard literature values (Vichi et al., brated to give reasonable agreement with the observational 2007, 2003, 2013; Fiori et al., 2012). The simulations were data. allowed to run out to steady state, and multi-year monthly As mentioned previously, oxygen is historically difficult means were calculated as functions of depth for chloro- to predict using BGC models of any complexity. It is likely phyll, oxygen, nitrate, phosphate, particulate organic nitro- that this is due, in part, to inaccuracies in the mixing pa- gen (PON), and net primary production (NPP), each of which rameterizations used in POM-1D and other physical models. was measured at the BATS/BTM site. The model PON is For example, BFM17 struggles to accurately predict oxygen, defined as the sum of nitrogen contained within the phyto- in part, because the second-order mixing scheme of Mellor plankton, zooplankton, and particulate detritus, and NPP is and Yamada(1982) lacks sufficient resolution of the winter defined as the net phytoplankton carbon uptake (or gross pri- mixing using just the monthly mean temperature and salin- mary production) minus phytoplankton respiration. ity. However, since it is often not included or presented at Figure4 qualitatively compares the BATS data (top row) all in models of similar complexity to BFM17 (i.e., models with the results from BFM17 (middle row). The model is reduced enough to reasonably couple to a high-fidelity, high- able to capture the initial spring bloom between January resolution physical model), studies that explore this hypothe- and March brought on by physical entrainment of nutrients, sis have been difficult to undertake. Thus, we include oxygen the corresponding peak in net primary production and PON in BFM17 and present our results here to illustrate this ex- around the same time, and the subsequent subsurface chloro- act point and to lend motivation to developing and using a phyll maxima during the summer (evident in Fig.4 as a larger model such as BFM17 to study the effects of physical pro- chlorophyll concentration at depths close to 100 m during the cesses missing from mixing parameterizations and how they summer months). The predicted oxygen levels are lower than can be better represented. observed values; however, the overall structure predicted by To obtain a first indication of the performance of BFM17, BFM17 is not completely dissimilar to that of the BATS a model assessment was performed for each target field. The oxygen field. These results are consistent with those from same assessment was performed for BFM56 to compare the BFM56 (bottom row of Fig.4), suggesting that the two mod- two models. The results are summarized by the Taylor dia- els are in generally close agreement. Correlation coefficients gram in Fig.5. This diagram can be used to assess the extent between the two models are 0.85 for chlorophyll, 0.56 for of misfit between the models and observations by showing oxygen, 0.99 for nitrate, 0.99 for phosphate, 0.95 for PON, the normalized root mean square errors (RMSEs), normal- and 0.97 for NPP. Differences in chlorophyll and oxygen are ized standard deviation, and the correlation coefficient be- likely due to the removal in BFM17 of specific phytoplank- tween each of the model outputs and the BATS target fields. ton and zooplankton species in favor of general LFGs, to The normalized RMSEs were calculated as εrms/σobs, the removal of denitrification, and to the parameterization where εrms is the RMSE between the model and the obser- of remineralization using new closure terms that were cali- vation fields and σobs is the standard deviation of the obser- vation field. The normalized standard deviation was calcu-

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Figure 4. Comparison of target BATS fields (a–f) to BFM17 simulation results (g–l) and BFM56 simulation results (m–r) for (a ,g, m) chloro- phyll (mg Chl a m−3), (b, h, n) oxygen (mmol O m−3), (c, i, o) nitrate (mmol N m−3), (d, j, p) phosphate (mmol P m−3), (e, k, q) particulate organic nitrogen (PON; mg N m−3), (f, l, r) and net primary production (NPP; mg C m−3 d−1). Simulation plots are multi-year monthly averages of the last 3 years of a 10-year integration.

lated as σmod/σobs, where σmod is the standard deviation of while NPP and PON have too little and too much variability, the model fields. The normalized RMSEs, normalized stan- respectively. dard deviation, and the correlation coefficients each give an Table3 provides a comparison of correlation coefficients indication of the relative similarities in amplitude, variations and un-normalized RMSEs, calculated with respect to the in amplitude, and structure of each modeled field compared observational fields, from BFM17 and BFM56, as well as to the BATS target fields, respectively. For each variable, from other models. Comparisons were only made to models these statistics were calculated over all months and all depths that were calibrated using the same BATS/BTM data, em- shown in Fig.4. ployed some kind of parameter estimation technique, and re- The Taylor diagram in Fig.5 shows that BFM17 and ported correlation and RMSEs. Ayata et al.(2013) included BFM56 produce similar results. For most variables, errors six biological tracers, while both Fasham et al.(1990) and in the amplitudes are within roughly one standard devia- Spitz et al.(2001) included seven. The Spitz et al.(2001) tion of the observations. Additionally, the structures of the study used data assimilation, while the Ayata et al.(2013) model fields for chlorophyll, nitrate, phosphate, PON, and and Fasham et al.(1990) studies used only optimization to NPP have high correlations with that of the BATS target determine a select set of parameters. All models used clima- fields. The correlation values range from 0.63 for chlorophyll tological monthly mean forcing from the BATS region and to 0.94 for nitrate in BFM17 and from 0.60 for chlorophyll reported climatological monthly means for their results. Care to 0.93 for phosphate and nitrate in BFM56. For BFM17, was taken to ensure that the same variable definition was variabilities in amplitude for nitrate, phosphate, oxygen, and compared between all models. Ayata et al.(2013) used a sim- NPP are closest to those of the corresponding BATS target ilar 1-D physical model to the one that was used here, while fields, while the chlorophyll and PON have too much vari- Spitz et al.(2001) and Fasham et al.(1990) used a time- ability. For BFM56, nitrate, phosphate, oxygen, and chloro- dependent box model of the upper-ocean mixed layer. As phyll have similar variability in amplitude to the BATS data, such, correlations and RMSE values for comparison to Ay- ata et al.(2013) were computed over the entire domain (Ay- https://doi.org/10.5194/gmd-14-2419-2021 Geosci. Model Dev., 14, 2419–2442, 2021 2430 K. M. Smith et al.: A reduced biogeochemical flux model

as the Spitz et al.(2001) model. The extra biological trac- ers in BFM17, as compared to the Ayata et al.(2013) and Fasham et al.(1990) models, account for variable intra- and extracellular nutrient ratios with the addition of phosphorus. Finally, a key benefit of the chemical functional family ap- proach used by BFM17 is the ability of the model to predict non-Redfield nutrient ratios. Figure6 shows the constituent component ratios normalized by the respective Redfield ra- tios for BFM17. The figure includes the component ratios of carbon to nitrogen, carbon to phosphorous, and nitrogen to phosphorous for phytoplankton, dissolved organic matter (DOM), and POM. Zooplankton nutrient ratios were not in- cluded because the parameterization of the zooplankton re- Figure 5. Taylor diagram showing the normalized standard devia- laxes the nutrient ratio back to a constant value. The normal- tion, correlation coefficient, and normalized root mean squared dif- ized ratio values are uniform non-unity-valued fields. ferences between the BFM17 output and the BATS target fields. Ultimately, Fig.6 shows that BFM17 is able to cap- Observations lie at (1,0). Radial deviations from observations cor- ture the phosphate-limited dynamics that characterize the respond to the normalized root mean square error (RMSE), radial BATS/BTM region (Fanning, 1992; Michaels et al., 1993; deviations from the origin correspond to the normalized standard deviation, and angular deviations from the vertical axis correspond Cavender-Bares et al., 2001; Steinberg et al., 2001; Ammer- to the correlation coefficient. BFM17 and BFM56 results are shown man et al., 2003; Martiny et al., 2013; Singh et al., 2015). as colored circles and triangles, respectively (chlorophyll is indi- In particular, Fig.6 shows that all results comparing carbon cated in blue, oxygen is indicated in orange, nitrate is indicated in or nitrogen to phosphorous for BFM17 produce normalized yellow, phosphate is indicated in purple, PON is indicated in green, values greater than 1, where the normalization is carried out and NPP is indicated in cyan). Note that BFM56 nitrate and phos- using the Redfield ratio (i.e., a normalized value greater than phate data points fall on top of one another (yellow and purple tri- 1 indicates that the field is denominator limited). Figure6 angles). also shows that the ratios are not uniform for phytoplankton, DOM, and POM, with the ratios decreasing with depth as a result of the increased availability of nitrogen and phosphate. ata et al., 2013, calculated their metrics over the top 168 m of their domain). For comparison to Spitz et al.(2001) and Fasham et al.(1990), correlations and RMSEs were calcu- 6 Conclusions lated only within the mixed layer (defined as the depth at which the density is 0.2 kgm−3 greater than the surface den- In this study, we have presented a new upper-thermocline, sity) and are shown as separate columns in Table3. open-ocean BGC model that is complex enough to capture The correlation coefficients and RMSEs for both BFM17 open-ocean ecosystem dynamics within the Sargasso Sea re- and BFM56 are comparable to the Ayata et al.(2013) study gion, yet reduced enough to integrate with a physical model for chlorophyll, while they outperform this study for nitrate, with limited additional computational cost. The new model, PON, and NPP. The Spitz et al.(2001) study, which used data named the Biogeochemical Flux Model 17 (BFM17), in- assimilation and is therefore naturally more likely to perform cludes 17 state variables and expands upon more reduced better, does in fact do so for predictions of chlorophyll and BGC models by incorporating a phosphate equation and nitrate. However, the nitrate correlation values for BFM17 tracking dissolved oxygen, as well as variable intra- and and the Spitz et al.(2001) model are both high, although extracellular nutrient ratios. BFM17 was developed primar- the latter model does have a lower RMSE value. As com- ily for use within high-resolution, high-fidelity 3-D physical pared to the Spitz et al.(2001) model, BFM17 has higher models, such as LES, for process, parameterization, and pa- correlation values for both PON and NPP but a larger RMSE rameter optimization studies, applications for which its more for NPP. Lastly, both BFM17 and BFM56 outperform the complex counterpart (BFM56) would be much too costly. Fasham et al.(1990) study for all fields for both correlation To calibrate and test the model, it was coupled to the coefficient and RMSE values. 1-D Princeton Ocean Model (POM-1D) and forced using These results show that, with a relatively small increase field data from the Bermuda Atlantic test site area. The full in the number of biological tracers as compared to simi- 56-state-variable Biogeochemical Flux Model (BFM56) was lar models, BFM17 is generally able to increase correlation also run using the same forcing. Results were compared be- coefficient values and decrease RMSE values for many of tween the two models and all six of the BATS target fields the target fields in comparison to similar models. Moreover, – chlorophyll, oxygen, nitrate, phosphate, PON, and NPP – BFM17 approaches the accuracy of models that use data as- and a model skill assessment was performed, concluding that similation to improve agreement with the observations, such the BFM17 captures the subsurface chlorophyll maximum

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Table 3. Correlation coefficients (and RMSE in parenthesis) between BATS target fields and model data for BFM17, BFM56, and several example models of similar complexity. The first set of BFM columns is calculated over the entire water column, while the second set (denoted with “ML only”) is calculated over the monthly mixed layer depth only (defined as the depth at which the density is 0.2 kgm−3 greater than the surface density).

Variable BFM17 BFM56 Ayata et al. (2013) BFM17 BFM56 Fasham et al. Spitz et al. (ML only) (ML only) (1990) (2001) Chlorophyll 0.63 (0.08) 0.60 (0.10) 0.60 (0.06) 0.63 (0.07) 0.60 (0.09) −0.33 (0.34) 0.86 (0.04) Oxygen 0.37 (31.18) 0.18 (21.84) – 0.29 (29.53) −0.09 (20.22) – – Nitrate 0.94 (0.22) 0.93 (0.16) 0.80 (0.33) 0.94 (0.22) 0.93 (0.15) 0.87 (0.28) 0.98 (0.05) Phosphate 0.91 (0.01) 0.93 (0.005) – 0.91 (0.01) 0.93 (0.005) – – PON 0.85 (0.15) 0.85 (0.11) 0.45 (0.08) 0.86 (0.14) 0.86 (0.10) 0.48 (0.6) 0.76 (0.12) NPP 0.93 (0.26) 0.87 (0.63) 0.50 (0.14) 0.94 (0.21) 0.89 (0.5) −0.47 (0.021) 0.69 (0.016)

Figure 6. Fields of BFM17 constituent component ratios of carbon to nitrogen (a–c), carbon to phosphorous (d–f), and nitrogen to phospho- rous (g–i) for phytoplankton (a, d, g), dissolved organic detritus (b, e, h), and particulate organic detritus (c, f, i). Each field is normalized by the respective Redfield ratio. and bloom intensity observed in the BATS data and produces fields. Additionally, it would be useful to study the efficacy comparable results to BFM56. In comparison with similar of using BFM17 in a global context, to reproduce the ecology studies using slightly less complex models, BFM17-POM- in other regions of the ocean, and its sensitivity under various 1D performs on par with, or better than, those studies. physical forcing scenarios. Finally, BFM17 is now of a size In the future, a sensitivity study is necessary to assess the that it can be efficiently integrated in high-resolution, high- most sensitive model parameters, both in BFM17 as well fidelity 3-D simulations of the upper ocean, and future work as in the 1-D physical model. After identification of these will examine model results in this context. most sensitive model parameters, an optimization can be per- formed to reduce discrepancies between the BATS obser- vational biology fields and the corresponding model output https://doi.org/10.5194/gmd-14-2419-2021 Geosci. Model Dev., 14, 2419–2442, 2021 2432 K. M. Smith et al.: A reduced biogeochemical flux model

Appendix A: BFM17 model equations A2 Phytoplankton equations

In the following, the detailed equations and their parame- The phytoplankton LFG in BFM17 is part of the living or- ter values for each of the 17 state variables that comprise ganic CFF and is composed of separate state variables for BFM17 are outlined. A summary of the 17 state variables is the constituents carbon, nitrogen, phosphorous, and chloro- provided in Table1 and a schematic of the CFFs and LFGs phyll, denoted PC, PN, PP, and Pchl, respectively (see also used in BFM17, along with their interactions, is shown in Table1). The governing equations for the constituent state Fig.1. It should be noted that for all BFM17 equations here, variables are given by we adopt the same notation style used for BFM56 in Vichi et al.(2007), Mussap et al.(2016), and the BFM user manual 1. the phytoplankton functional group in the living organic (Vichi et al., 2013) for consistency and clarity. CFF, carbon constituent (state variable PC): gpp rsp lys A1 Environmental parameters ∂PC ∂PC ∂PC ∂PC = − − ∂t ∂t ∂t ∂t (1) bio CO2 CO2 R BFM17 is influenced by the environment through tempera- C lys exu prd ture and irradiance. Temperature directly affects all physio- ∂PC ∂PC ∂PC − − − , (A5) logical processes and is represented in the model by intro- ∂t R(2) ∂t R(1) ∂t Z (T ) C C C ducing the non-dimensional parameter fj defined as − ∗ ∗ 2. the phytoplankton functional group in the living organic f (T ) = Q(T T )/T , j = P,Z, (A1) j 10,j CFF, nitrogen constituent (state variable PN): ∗ where T is a base temperature and Q10,j is a coefficient that " upt upt # may differ for the phytoplankton and zooplankton LFGs, de- ∂PN ∂PN ∂PN = max 0, + noted Pi and Zi, respectively. Here, the subscript i is used ∂t bio ∂t N(2) ∂t N(3) to denote different chemical constituents (i.e., C, N, and P) lys lys prd j ∂PN ∂PN ∂PN and is used to denote different LFGs. Base values used for − − − , (A6) T ∗ and Q are shown in Table A1. The model addition- ∂t (1) ∂t (2) ∂t 10,j RN RN ZN ally employs a temperature-dependent nitrification parameter (T ) fN , which is defined similarly to Eq. (A1) as 3. the phytoplankton functional group in the living organic ∗ ∗ CFF, phosphorus constituent (state variable P ): (T ) = (T −T )/T P fN Q10,N , (A2) " upt # lys where Q10,N is given in Table A1. ∂PP ∂PP ∂PP = max 0, − In contrast to temperature, irradiance only directly affects ∂t bio ∂t N(1) ∂t R(1) phytoplankton, serving as the primary energy source for phy- P lys prd toplankton growth and maintenance. Irradiance is a func- ∂PP ∂PP − − , (A7) tion of the incident solar radiation at the sea surface. Within ∂t (2) ∂t RP ZP BFM17, the amount of PAR at any given location z is param- eterized according to the Beer–Lambert model as 4. the phytoplankton functional group in the living organic  0  CFF, chlorophyll constituent (state variable P ): Z chl 0 0 EPAR(z) = εPARQS expλwz + λbio(z )dz  , (A3) syn loss ∂Pchl ∂Pchl ∂Pchl z = − , (A8) ∂t bio ∂t ∂t where QS is the shortwave surface irradiance flux, which is typically obtained from real-world measurements of the where the descriptions of each of the source and sink terms atmospheric radiative transfer, εPAR is the fraction of PAR are provided in Table A2. The subscript “bio” on the left- within QS, λw is the background light extinction due to wa- hand-side terms indicates that these are the total rate expres- ter, and λbio is the light extinction due to suspended biologi- sions associated with all biological processes. cal particles. Values for εPAR and λw are given in Table A1. For the evolution of the phytoplankton carbon constituent The extinction coefficient due to particulate matter, λbio, is given by Eq. (A5), gross primary production depends on the dependent on phytoplankton chlorophyll, Pchl, and particu- (2) non-dimensional regulation factors for temperature and light late detritus, RC , and is written as as well as on the maximum photosynthetic growth rate and (2) the phytoplankton carbon instantaneous concentration. This λbio = cP Pchl + c (2) R , (A4) R C then gives where cP and c (2) are the specific absorption coefficients R gpp of phytoplankton chlorophyll and particulate detritus, respec- ∂PC (0) (T ) (E) = r f f PC , (A9) tively, with values given in Table A1. ∂t P P P CO2

Geosci. Model Dev., 14, 2419–2442, 2021 https://doi.org/10.5194/gmd-14-2419-2021 K. M. Smith et al.: A reduced biogeochemical flux model 2433

Table A1. Symbols, values, units, and descriptions for environmental parameters within the BFM17 pelagic model.

Symbol Value Units Description

Q10,P 2.00 – Phytoplankton Q10 coefficient Q10,Z 2.00 – Zooplankton Q10 coefficient Q10,N 2.00 – Nitrification Q10 coefficient T ∗ 10.0 ◦C Base temperature 2 −1 cP 0.03 m (mg Chl) Chlorophyll-specific light absorption coefficient εPAR 0.40 – Fraction of photosynthetically active radiation −1 λw 0.0435 m Background attenuation coefficient −3 2 −1 cR(2) 0.1 × 10 m (mg C) C-specific attenuation coefficient of particulate detritus

Table A2. List of abbreviations used to indicate physiological where bP is the basal specific respiration rate, γP is the and ecological processes in the equations comprising the BFM17 respired fraction of the gross primary production, the gross pelagic model. primary production term is given by Eq. (A9), and the ex- udation term is defined below in Eq. (A18). Values and de- Abbreviation Process scriptions for bP and γP are given in Table A3. gpp Gross primary production Both phytoplankton exudation and lysis, defined below, (N,P) rsp Respiration depend on a multiple nutrient limitation term fP . This prd Predation term allows for the internal storage of nutrients and depends rel Biological release: egestion, excretion, mortality on the respective nutrient limitation terms for both nitrate and exu Exudation h i phosphate. It is given by f (N,P) = min f (N),f (P) , where upt Uptake P P P lys Lysis ( " #) P /P − φ(min) syn Biochemical synthesis (N) = N C N fP min 1,max 0, , (A13) loss Biochemical loss φ(opt) − φ(min) nit Nitrification N N ( " (min) #) PP/PC − φ f (P) = min 1,max 0, P . (A14) P (opt) − (min) φP φP r(0) where P is the maximum photosynthetic rate for phyto- (opt) (opt) (T ) φ φ plankton (reported in Table A3) and f is the temperature- The parameters N and P are the optimal phytoplank- P ton quotas for nitrogen and phosphorus, respectively, while regulating factor for phytoplankton given by Eq. (A1). The (min) (min) (E) φ φ term f is the light regulation factor for phytoplankton, N and P are the minimum possible quotas, below P (N) (P) which is defined following Jassby and Platt(1976) as which fP and fP are zero. Values for each of these pa- rameters are included in Table A3.  E  (E) = − − PAR Phytoplankton lysis includes all mortality due to mechan- fP 1 exp , (A10) EK ical, viral, and yeast cell disruption processes, and is parti- tioned between particulate and dissolved detritus. The inter- where EPAR is defined in Eq. (A3) and EK (the “optimal” nal cytoplasm of the cell is released to dissolved detritus, de- irradiance) is given by (1) noted by Ri , while structural parts of the cell are released to " (0) # (2) r  P  particulate detritus, denoted by the state variable Ri , where E = P C . (A11) K (0) i = C,N,P (see also Table1). The resulting lysis terms in Pchl αchl Eqs. (A5)–(A7) are then given by " # The parameter α(0) is the maximum light utilization coeffi- ∂P lys h i h(N,P) chl i = 1 − ε(N,P) P d(0)P , cient and is defined in Table A3. P (N,P) (N,P) P i ∂t R(1) f + h Phytoplankton respiration is parameterized in Eq. (A5) as i P P the sum of the basal respiration and activity respiration rates, i = C,N,P, (A15) " # namely ∂P lys h(N,P) i = (N,P) P (0) εP dP Pi , rsp ∂t (2) (N,P) + (N,P) ∂PC (T ) Ri fP hP = bP f PC ∂t P CO2 i = C,N,P, (A16) " gpp exu # (N,P) (0) ∂PC ∂PC where h is the nutrient-stress threshold and d is the + γP − , (A12) P P ∂t ∂t (1) maximum specific nutrient-stress lysis rate, both of which are CO2 RC https://doi.org/10.5194/gmd-14-2419-2021 Geosci. Model Dev., 14, 2419–2442, 2021 2434 K. M. Smith et al.: A reduced biogeochemical flux model

Table A3. Phytoplankton parameters, values, units, and descriptions within the BFM17 pelagic model.

Symbol Value Units Description

(0) −1 rP 1.60 d Maximum specific photosynthetic rate −1 bP 0.05 d Basal specific respiration rate (0) −1 dP 0.05 d Maximum specific nutrient-stress lysis rate (N,P) hP 0.10 – Nutrient-stress threshold βP 0.05 – Excreted fraction of primary production γP 0.05 – Activity respiration fraction (N) 3 −1 −1 aP 0.025 m (mg C) d Specific affinity constant for nitrogen (N) −3 hP 1.50 mmol N-NH4 m Half-saturation constant for ammonium uptake (min) × −3 −1 φN 6.87 10 mmol N (mg C) Minimum nitrogen quota (opt) × −2 −1 φN 1.26 10 mmol N (mg C) Optimal nitrogen quota (max) (opt) −1 φN 1.0φN mmol N (mg C) Maximum nitrogen quota (P) × 3 3 −1 −1 aP 2.5 10 m (mg C) d Specific affinity constant for phosphorus (min) × −4 −1 φP 4.29 10 mmol P (mg C) Minimum phosphorus quota (opt) × −4 −1 φP 7.86 10 mmol P (mg C) Optimal phosphorus quota (max) (opt) −1 φP 1.0φP mmol P (mg C) Maximum phosphorus quota (0) × −5 −1 −1 2 αchl 1.52 10 mg C (mg Chl) (µE) m Maximum light utilization coefficient (0) −1 θchl 0.016 mg Chl (mg C) Maximum chlorophyll-to-carbon quota

(N,P) given in Table A3. The term εP is a fraction that ensures growth needs and any excess uptake, namely nutrients within the structural parts of the cell, which are less ( " # degradable, are always released as particulate detritus. This ∂P upt h(N) N = min a(N) P N (2) + N (3) P , fraction is determined by the expression P (N) C ∂t (2,3) + (3) N hP N (max) " # φ GP φ(min) φ(min) N ε(N,P) = min 1, N , P , (A17)  P   P + (max) − N PN/PC PP/PC νP φN PC , PC (A19) where φ(min) and φ(min) are given in Table A3. N P where a(N) is the specific affinity for nitrogen, h(N) is the If phytoplankton cannot equilibrate their fixed carbon with P P (max) sufficient nutrients, this carbon is not assimilated and is in- half-saturation constant for ammonium uptake, and φN is stead released in the form of dissolved carbon, denoted by the maximum nitrogen quota; base values for these three pa- (1) rameters are given in Table A3. The net primary productivity state variable RC , in a process known as exudation. The ex- udation term in Eq. (A5) is parameterized as GP in Eq. (A19) is given as " ∂P gpp ∂P exu exu gpp = C − C ∂PC n h io ∂PC GP max 0, = β + (1 − β ) 1 − f (N,P) , (A18) ∂t ∂t (1) P P P CO2 RC ∂t R(1) ∂t CO C 2 rsp lys lys # ∂PC ∂PC ∂PC − − − . (A20) ∂t ∂t (1) ∂t (2) where βP is the excreted fraction of gross primary produc- CO2 RC RC tion, defined in Table A3, and the gross primary production The specific uptake rate ν appearing in Eq. (A19) is given term is again given by Eq. (A9). P by The nutrient uptake of Eqs. (A6) and (A7) combines both the intracellular quota (i.e., Droop) and external concentra- = (T) (0) νP fP rP . (A21) tion (i.e., Monod) approaches (Baretta-Bekker et al., 1997). The total phytoplankton uptake of nitrogen, represented by It should be noted that only the sum of the two uptake terms, the combination of the two uptake terms in Eq. (A6), is the represented by Eq. (A19), is required in the governing equa- minimum of a diffusion-dependent uptake rate when internal tion for PN given by Eq. (A6). However, in the governing nutrient quotas are low and a rate that is based upon balanced equations for nitrate and ammonium, denoted N (2) and N (3)

Geosci. Model Dev., 14, 2419–2442, 2021 https://doi.org/10.5194/gmd-14-2419-2021 K. M. Smith et al.: A reduced biogeochemical flux model 2435

(see Table1) that will be presented later, expressions are re- the phytoplankton contribution to the extinction coefficient quired for the individual uptake portions from nitrate and am- in Eq. (A4). The phytoplankton chlorophyll source term in monium. When the total phytoplankton nitrogen uptake rate Eq. (A8) is made up of only two terms: chlorophyll synthesis from Eq. (A19) is positive, the individual portions from ni- and loss. Net chlorophyll synthesis is a function of acclima- trate and ammonium are determined by tion to light conditions, availability of nutrients, and turnover rate, and is given by ∂P upt ∂P upt N = ε N , (A22) " # P ∂P syn ∂P gpp ∂P exu ∂t N(2) ∂t N(2,3) chl C C = ρchl (1 − γP ) − upt upt ∂t ∂t ∂t R(1) ∂PN ∂PN CO2 C = (1 − εP ) , (A23) ∂t (3) ∂t (2,3) " lys lys N N Pchl ∂PC ∂PC − + PC ∂t (1) ∂t (2) where the rates on the right-hand sides are obtained from RC RC Eq. (A19), and εP is given as rsp # ∂PC + , (A28) s N (2) ∂t CO ε = N . (A24) 2 P (3) (2) N + sNN where ρchl regulates the amount of chlorophyll in the phy- The preference for ammonium is defined by the saturation toplankton cell and all other terms in the above expression function sN and is given by have been defined previously. The term ρchl is computed ac- cording to a ratio between the realized photosynthetic rate (N) (i.e., gross primary production) and the maximum potential hP sN = . (A25) photosynthesis (Geider et al., 1997), and is correspondingly h(N) + N (3) P given as

When the phytoplankton nitrogen uptake rate from Eq. (A19) ( " gpp (0) (1 − γP ) ∂PC is negative, however, the entire nitrogen uptake goes to the ρchl = θ min 1, (1) chl (0) ∂t dissolved organic nitrogen pool, RN (see Eq. A42). αchl EPARPchl CO2 As with the uptake of nitrogen, phytoplankton uptake of exu #) ∂PC phosphorus in Eq. (A7) is the minimum of a diffusion- − , (A29) ∂t (1) dependent rate and a balanced growth/excess uptake rate. RC This uptake comes entirely from one pool and the uptake (0) term in Eq. (A7) is correspondingly given by where θchl is the maximum chlorophyll-to-carbon quota and α(0) is the maximum light utilization coefficient, both of ∂P upt n chl P = (P) (1) (max) which can be found in Table A3. Chlorophyll loss in Eq. (A8) min aP N PC , φP GP ∂t N(1) is simpler and is just a function of predation, where the h io amount of chlorophyll transferred back to the infinite sink is +ν φ(max)P − P , (A26) P P C P proportional to the carbon predated by zooplankton, giving

(P) loss prd where a is the specific affinity constant for phosphorous ∂Pchl Pchl ∂PC P = . (A30) (max) ∂t P ∂t and φP is the maximum phosphorous quota. Values for C ZC both parameters are given in Table A3. If the uptake rate is negative, the entire phosphorus uptake goes to the dissolved A3 Zooplankton equations organic phosphorus pool, R(1). P The zooplankton LFG group in BFM17 is part of the living Predation of phytoplankton within BFM17 is solely per- organic CFF and is composed of separate state variables for formed by zooplankton, and each of the predation terms ap- carbon, nitrogen, and phosphorous, denoted Z , Z , and Z , pearing in Eqs. (A5)–(A7) are equal and opposite to the zoo- C N P respectively (see also Table1). The governing equations for plankton predation terms, namely the constituent state variables are given by prd prd ∂Pi ∂Zi 5. the zooplankton functional group in the living organic = − , i = C,N,P. (A27) ∂t ∂t Zi Pi CFF, carbon constituent (state variable ZC): Equations for the zooplankton predation terms are given in ∂Z ∂Z prd ∂Z rsp C = C − C the next section. ∂t bio ∂t P ∂t CO Finally, phytoplankton chlorophyll, denoted P with the C 2 chl rel rel rate equation given by Eq. (A8), contributes to the defini- ∂ZC ∂ZC − − , (A31) tion of the optimal irradiance value in Eq. (A11) and of ∂t (1) ∂t (2) RC RC https://doi.org/10.5194/gmd-14-2419-2021 Geosci. Model Dev., 14, 2419–2442, 2021 2436 K. M. Smith et al.: A reduced biogeochemical flux model

6. the zooplankton functional group in the living organic the sum of a constant mortality rate and an oxygen-dependent CFF, nitrogen constituent (state variable ZN): regulation factor given by

prd rel (O) O ∂ZN ∂ZN ∂ZN f = , (A36) = − A + (O) ∂t ∂t ∂t (1) O hA bio PN RN rel rel ∂ZN ∂ZN where the subscript A is either Z for zooplankton or N for − − , (A32) nitrification, O represents the oxygen constituents of the ∂t (2) ∂t (3) RN N (O) dissolved gas in the inorganic CFF, and hA is the half- saturation coefficient for either zooplankton (subscript A = 7. the zooplankton functional group in the living organic Z) processes or chemical (subscript A = N) processes given CFF, phosphorus constituent (state variable ZP): in Tables A4 and A5, respectively. The total biological re- prd rel lease is then partitioned into particulate and dissolved or- ∂ZP ∂ZP ∂ZP = − ganic matter, giving ∂t ∂t P ∂t R(1) bio P P ( ∂Z rel ∂Z prd rel rel i = (i) i + ∂ZP ∂ZP εZ βZ dZ − − , (A33) ∂t (1) ∂t R Pi ∂t R(2) ∂t N(1) i P h i o + (0) − (O) (T ) = dZ 1 fZ fZ Zi , i C,N,P, (A37) where, once more, descriptions of each of the source and sink ∂Z rel h i ∂Z rel terms are provided in Table A2. i = − (i) i = 1 εZ , i C,N,P, (A38) ∂t (2) ∂t (1) Zooplankton predation of phytoplankton, which appears Ri Ri as the first term in each of Eqs. (A31)–(A33), primarily de- (i) pends on the availability of phytoplankton and their capture where εZ is the fraction excreted to the dissolved pool, dZ is efficiency, and is expressed as (0) the specific mortality rate, and dZ is the oxygen-dependent   specific morality rate. Base values for each parameter are ∂Z prd P P given in Table A4. i = i (T ) (0) C fZ rZ ZC , ∂t P (F) (PC+µZ) The zooplankton also excrete into the nutrient pools of PC C PC + h Z δZ,P phosphate, N (1), and ammonium, N (3). These effects are rep- i = C,N,P, (A34) resented by the final terms of Eqs. (A32) and (A33), which are parameterized by where r(O) is the potential specific growth rate, h(F) is the Z Z rel   ∂ZN ZN Michaelis constant for total food ingestion, and µZ is the = (N) − (opt) νZ max 0, ϕN ZN , (A39) feeding threshold. These parameters and their base values ∂t N(3) ZC (T ) rel are included in Table A4. Here, fZ is the temperature- ∂Z  Z  P = (P) P − (opt) regulating factor for zooplankton growth given by Eq. (A1). νZ max 0, ϕP ZP , (A40) ∂t N(1) ZC The total food availability can be expressed as δZ,P PC, where δZ,P is the prey availability of phytoplankton and is (N) (P) (opt) where νZ and νZ are specific rate constants and ϕN and included in Table A4. (opt) Zooplankton respiration is the sum of active and basal ϕP are the optimal zooplankton quotas for nitrogen and metabolism rates, where active respiration is the cost of nu- phosphorous, respectively. All four parameters are included trient ingestion, or predation. The resulting respiration rate is in Table A4. given by A4 Dissolved organic matter equations rsp prd ∂ZC ∂ZC (T ) The governing equations for the three constituents of dis- = (1 − ηZ − βZ) + bZf ZC , (A35) ∂t ∂t Z CO2 Pc solved organic matter are given by where ηZ is the assimilation efficiency, βZ is the excreted 8. dissolved matter in non-living organic CFF, carbon con- (1) fraction uptake, and bZ is the basal specific respiration rate. stituent [state variable RC ]: All three parameters are included in Table A4. ∂R(1) ∂P lys ∂P exu The biological release terms in Eqs. (A31)–(A33) are the C = C + C sum of zooplankton excretion, egestion, and mortality. Ex- ∂t ∂t R(1) ∂t R(1) cretion and egestion are the portions of ingested nutrients, re- bio C C ∂Z rel sulting from predation, that have not been assimilated or used + C − (sinkC) (1) α (1) RC , (A41) for respiration. Zooplankton mortality is parameterized as ∂t (1) R RC

Geosci. Model Dev., 14, 2419–2442, 2021 https://doi.org/10.5194/gmd-14-2419-2021 K. M. Smith et al.: A reduced biogeochemical flux model 2437

Table A4. Zooplankton parameters, values, units, and descriptions within the BFM17 pelagic model.

Symbol Value Unit Description

(O) −3 hZ 0.5 mmol O2 m Half saturation for zooplankton processes −3 µZ 50.0 mg C m Feeding threshold −1 bZ 0.02 d Basal specific respiration rate (0) −1 rZ 2.00 d Potential specific growth rate (0) −1 dZ 0.25 d Oxygen-dependent specific mortality rate −1 dZ 0.05 d Specific mortality rate ηZ 0.50 – Assimilation efficiency βZ 0.25 – Fraction of activity excretion C εZ 0.60 – Partition between dissolved and particulate excretion of C N εZ 0.72 – Partition between dissolved and particulate excretion of N P εZ 0.832 – Partition between dissolved and particulate excretion of P (F ) −3 hZ 200.0 mg C m Michaelis constant for total food ingestion δZ,P 1.00 – Availability of phytoplankton to zooplankton (P) −1 νZ 1.0 d Specific rate constant for phosphorous excretion (N) −1 νZ 1.0 d Specific rate constant for nitrogen excretion (opt) × −4 −1 ϕP 7.86 10 mmol P (mg C) Optimal phosphorous quota (opt) −1 ϕN 0.0126 mmol N (mg C) Optimal nitrogen quota

9. dissolved matter in non-living organic CFF, nitrogen A5 Particulate organic matter equations (1) constituent [state variable RN ]: The governing equations for the three constituents of partic- (1) lys rel ∂RN ∂PN ∂ZN ulate organic matter are given by = + ∂t ∂t (1) ∂t (1) bio RN RN 11. particulate matter in non-living organic CFF, carbon (2) " upt upt # ∂P ∂P constituent [state variable RC ]: − min 0, N + N

∂t N(2) ∂t N(3) ∂R(2) ∂P lys ∂Z rel C = C + C (1) − ζ (3) R , (A42) ∂t ∂t (2) ∂t (2) N N bio RC RC − (sinkC) (2) 10. dissolved matter in non-living organic CFF, phosphorus α (2) RC , (A44) (1) R constituent [state variable RP ]: 12. particulate matter in non-living organic CFF, nitrogen (1) lys rel (2) ∂R ∂PP ∂ZP P = + constituent [state variable RN ]:

∂t ∂t R(1) ∂t R(1) bio P P (2) lys rel ∂RN ∂PN ∂ZN " upt # = + ∂PP (1) (2) (2) − − ∂t ∂t R ∂t R min 0, ζN(1) RP . (A43) bio N N ∂t N(1) − (2) ξN(3) RN , (A45) All terms except for the last terms in each of these equations, representing remineralization, have been defined in previ- 13. particulate matter in non-living organic CFF, phospho- (2) ous sections. Remineralization of dissolved organic matter rus constituent [state variable RP ]: by bacteria is parameterized within BFM17 as a rate that ∂R(2) ∂P lys ∂Z rel is proportional to the local concentration of that dissolved P = P + P − (2) ξN(1) RP . (A46) constituent. In Eq. (A41), remineralization is parameterized ∂t ∂t (2) ∂t (2) bio RP RP as α(sinkC)R(1), where α(sinkC) is a constant that controls the R(1) C R(1) rate at which dissolved carbon is remineralized and returned Once again, all terms except for the final remineralization to the pool of carbon; this constant is given in Table A5. In terms in each equation have been defined in previous sec- Eqs. (A42) and (A43), remineralization is represented by the tions. Remineralization of particular organic matter by bac- parameters ζN(3) and ζN(1) , which are the specific remineral- teria is parameterized within BFM17 as a rate that is pro- ization rates of dissolved ammonium and phosphate, respec- portional to the local concentration of that particulate con- tively. These rates are also included in Table A5. stituent. In Eq. (A44), remineralization is parameterized by https://doi.org/10.5194/gmd-14-2419-2021 Geosci. Model Dev., 14, 2419–2442, 2021 2438 K. M. Smith et al.: A reduced biogeochemical flux model

Table A5. Values, units, and descriptions for dissolved organic matter, particulate organic matter, and nutrient parameters within the BFM17 pelagic model.

Symbol Value Units Description

α(sinkC) 0.05 d−1 Specific remineralization rate of dissolved carbon R(1) −1 ζN(1) 0.05 d Specific remineralization rate of dissolved phosphorus −1 ζN(3) 0.05 d Specific remineralization rate of dissolved nitrogen α(sinkC) 0.1 d−1 Specific remineralization rate of particulate carbon R(2) −1 ξN(1) 0.1 d Specific remineralization rate of particulate phosphorus −1 ξN(3) 0.1 d Specific remineralization rate of particulate nitrogen 3(nit) 0.01 d−1 Specific nitrification rate at 10 ◦C N(3) (O) −3 hN 10.0 mmol O2 m Half saturation for chemical processes (O) −1 C 12.0 mmol O2 mg C Stoichiometric coefficient for oxygen reaction (O) −1 N 2.0 mmol O2 mmol N Stoichiometric coefficient for nitrification reaction

α(sinkC)R(2), where α(sinkC) is a constant that controls the rate 16. dissolved nutrient in the inorganic CFF, nitrate con- R(2) C R(2) at which the particulate carbon is remineralized. The base stituent (state variable N (2)): value for this constant is provided in Table A5. The parame- nit (2) upt (2) ters ξN(3) and ξN(1) are the specific remineralization rates of ∂N ∂PN ∂N = − + , (A49) particulate ammonium and phosphate, respectively. The spe- ∂t ∂t (2) ∂t N (3) cific remineralization rates for particulate organic matter are bio N also presented in Table A5. 17. dissolved nutrient in the inorganic CFF, ammonium (3) A6 Dissolved gas and nutrient equations constituent (state variable N ):

∂N (3) ∂P upt The only dissolved gas resolved by BFM17 is oxygen, O = − N + (1) + (2) ζN(3) RN ξN(3) RN ∂t ∂t (3) (carbon dioxide is treated as an infinite source/sink), and the bio N (1) nit dissolved nutrients in the model are phosphate, N , nitrate, rel (3) (2) (3) ∂ZN ∂N N , and ammonium, N (see also Table1). Governing + − . (A50) ∂t (3) ∂t equations for each of these state variables are given by N N(2) 14. dissolved gas in the inorganic CFF, oxygen constituent Aeration of the surface layer by wind, ∂O/∂t|wind, is param- (state variable O): eterized as described in Wanninkhof(1992, 2014). In a 0-D wind " gpp rsp model, it is a source term for dissolved oxygen and thus be- ∂O ∂O (O) ∂PC ∂PC = +  − longs in Eq. (A47). However, in any model of one dimension ∂t ∂t C ∂t ∂t bio CO2 CO2 or more, it should be treated as a surface boundary condition rsp # for dissolved oxygen and thus belongs in Eq. (17) and should ∂ZC (sinkC) (2) (sinkC) (1) (O) (O) − − α ( ) R − α ( ) R be omitted from Eq. (A47). The parameters  and  ∂t R 2 C R 1 C C N CO2 are stoichiometric coefficients used to convert units of car- nit bon to units of oxygen and nitrogen, respectively. All terms ∂N (3) − (O) , in the above equations have been defined in previous sec- N ∂t N(2) tions, except for nitrification. Nitrification is a source term (A47) for nitrate and is parameterized as a sink of ammonium and oxygen as 15. dissolved nutrient in the inorganic CFF, phosphate con- nit nit stituent (state variable N (1)): ∂N (2) ∂N (3) = = 3(nit) f (T )f (O)N (3) , (A51) ∂t ∂t N(3) N N ∂N (1) ∂P upt N(3) N(2) = − P

∂t ∂t N(1) where 3(nit) is the specific nitrification rate, given in Ta- bio N(3) rel (T ) (O) (1) (2) ∂ZP ble A5. The terms fN and fN are defined in Eqs. (A2) + ζ (1) R + ξ (1) R + , N P N P (A48) and (A36), respectively. ∂t N(1)

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Appendix B: Zero-dimensional test of BFM17 Initial values for chlorophyll, oxygen, phosphate, and ni- trate were taken to be similar to values from the BATS/BTM −3 As a simple test without the influence of any particular phys- observational data, with Pchl = 0.2 mg Chl a m , O = −3 (1) −3 (2) ical model (as discussed previously, the choice of physical 230 mmol O2 m , N = 0.06 mmol P m , and N = model can greatly affect the results), BFM17 was integrated 1.0 mmol N m−3). Phytoplankton carbon was calculated us- in a 0-D (i.e., time-only) test for 10 years using sinusoidal ing the maximum chlorophyll-to-carbon ratio, θ (0) in Ta- ◦ chl forcing for the temperature (in units of C), salinity (psu), ble A3. Initial values for zooplankton carbon, dissolved car- − − 10 m wind speed (ms 1), and PAR (Wm 2) cycles. This bon, and particulate organic carbon were assumed to be the forcing is implemented as same as the phytoplankton carbon. Ammonium was assumed to have the same initial concentration as phosphate. All other (var) h (var) (var)i F (t) = Fs + Fw constituents were calculated using their respective optimal ratios in Tables A3 and A4. h (var) (var)i − 0.5 Fs − Fw cos(tR) , (B1) Figure B1 shows the seasonal cycle of surface chlorophyll, zooplankton carbon, and nitrate over the last 4 years of the where F (var) is the annually varying forcing term, “var” 10-year simulation period, indicating that a stable seasonal indicates the variable of interest, corresponding to temper- cycle with reasonable ecosystem values can be attained by ature (“temp”), salinity (“sal”), wind speed (“wind”), and the model, regardless of its coupling to a physical model. (var) (var) PAR. In Eq. (B1), Fw and Fs are, respectively, the Figure B1a and c also show monthly averaged values taken winter and summer extreme values for the forcing term from the observational data described in Sect.4. Although considered, 0 ≤ t ≤ 360 is the time, and R = π/180. The the agreement between the 0-D BFM17 model and the ob- winter and summer values were chosen to be similar to servations is not perfect, both are qualitatively similar and those found in the observational data described in Sect.4, close in magnitude, providing confidence in the accuracy of (temp) (temp) ◦ ◦ (sal) (sal) with [Fw ,Fs ] = [10 C,30 C], [Fw ,Fs ] = the model despite the lower fidelity of the 0-D test. (wind) (wind) −1 [37psu,36.5psu], [Fw ,Fs ] = [6,2ms ], and (PAR) (PAR) −2 [Fw ,Fs ] = [10,120Wm ]. The exact observa- tional data were not used, and instead we used an idealized version of the data for simplicity and because there is no physical variable in the 0-D framework to properly apply the exact observations. Note that, in the 0-D framework, the wind forcing does not constrain the biogeochemical dynamics but does play a role in oxygen exchange with the atmosphere, defined according to Wanninkhof(1992, 2014).

Figure B1. Seasonal cycle of surface (a) chlorophyll, (b) zooplankton carbon, and (c) nitrate from the 0-D test of BFM17. Results are shown for the last 4 years of the 10-year simulation. Panels (a) and (c) show monthly averaged values taken from the observational data described in Sect.4.

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Code and data availability. Current versions of BFM17 and Anderson, T. R.: Plankton functional type modelling: running be- BFM56 can be found at https://github.com/marco-zavatarelli/ fore we can walk?, J. Plankton Res., 27, 1073–1081, 2005. BFM17-56/tree/BFM17-56 (last access: 5 December 2020) under Ayata, S. D., Levy, M., Aumont, O., Siandra, A., Sainte-Marie, J., GNU General Public License version 3. The exact versions of the Tagliabue, A., and Bernard, O.: Phytoplankton growth formula- models used to produce the results used in this paper are archived tion in marine ecosystem models: Should we take into account on Zenodo at https://doi.org/10.5281/zenodo.3839984(Smith et photo-acclimation and variable stoichiometry in oligotrophic ar- al., 2020). Data and scripts used to produce all figures in this paper eas?, J. Marine Syst., 125, 29–40, 2013. are archived on Zenodo at https://doi.org/10.5281/zenodo.3840562 Baretta-Bekker, J. G., Baretta, J. 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Niemeyer were supported by NSF OAC-1535065 and OCE- Geophysical Union, 1–6, 1987. 1924658. The data analyzed in this paper are available at Zen- Boyd, P. W., Cornwall, C. E., Davison, A., Doney, S. C., Fourquez, odo, https://doi.org/10.5281/zenodo.3839984(Smith et al., 2020). M., Hurd, C. L., Lima, I. D., and McMinn, A.: Biological re- This work utilized the RMACC Summit supercomputer supported sponses to environmental heterogeneity under future ocean con- by NSF (ACI-1532235, ACI-1532236), CU-Boulder, and CSU, ditions, Global Change Biol., 22, 2633–2650, 2016. as well as the Yellowstone (ark:/85065/d7wd3xhc) and Cheyenne Cavender-Bares, K. K., Karl, D. M., and Chisholm, S. W.: Nutrient (https://doi.org/10.5065/D6RX99HX) supercomputers provided by gradients in the western North Atlantic Ocean: Relationship to NCAR CISL, sponsored by NSF. microbial community structure and comparison to patterns in the Pacific Ocean, Deep-Sea Res. Pt. I, 48, 2373–2395, 2001. Clainche, Y. 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